Chaotic and hypercyclic properties of the quasi-linear Lasota equation

• Autorzy: Cheng-Hung Hung
• Języki publikacji: EN

Abstrakty

EN

In this paper we describe an explicit solution semigroup of the quasi-linear Lasota equation. By constructing the relationship of this solution semigroup with the translation semigroup we obtain some sufficient and necessary conditions for the solution semigroup of the quasi-linear Lasota equation to be hypercyclic or chaotic respectively.

Słowa kluczowe

EN

Lasota equation; C0-semigroup

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2014-09-13

zaakceptowano

2015-05-10

online

2015-06-02

Twórcy

autor

Cheng-Hung Hung

• Cheng Shiu University, No.840, Cheng Cing Rd., Kaohsiung 833, Taiwan, R.O.C.

Bibliografia

• ---
• [1] Batty C. J. K., Derivations on the line and flow along orbits, Pacific Journal of Mathmatics, Vol 126, No 2, 1987, 209-225.
• [2] Brunovsky P. and Komornik J., Ergodicity and exactness of the shift on C[0;1) and the semiflow of a first order partial differential equation, J. Math. Anal. Appl., 104 (1984), 235–245.
• [3] Chang Y.-H. and Hong C.-H., "The chaos of the solution semigroup for the quasi-linear lasota equation," Taiwanese Journal of Mathematics, vol. 16, no. 5, pp. 1707–1717, 2012.
• [4] Dawidowicz A. L., Haribash N. and Poskrobko A., On the invariant measure for the quasi-linear Lasota equation, Math. Meth. Appl. Sci., 2007, 30, 779-787. [WoS]
• [5] Desch W., Schappacher W. and Webb G. F., Hypercyclic and chaotic semigroups of linear operators, Ergodic Theory Dynamical Systems, 17 (1997), 793–819.
• [6] Hung C.-H. and Chang Y.-H. "Frequently Hypercyclic and Chaotic Behavior of Some First-Order Partial Differential Equation, "Abstract and Applied Analysis Volume 2013, Article ID 679839. [WoS]
• [7] Lasota A., Stable and chaotic solutions of a first-order partial differential equation, Nonlinear Analysis 1981 5, 1181–1193.
• [8] Lasota A. and Szarek T., Dimension of measures invariant with respect to the Wa’zewska partial differential equation, J. Differential Equations, 196, 2004, 448-465.
• [9] Mackey M. C. and Schwegle H., Ensemble and trajectory statistics in a nonlinear partial differential equation, Journal of Statistical Physics, Vol. 70, Nos. 1/2, 1993.
• [10] Matsui M. and Takeo F., Chatoic semigroups generated by certain differential operators of order 1, SUT Journal of Mathmatics, Vol 37, 2001, 43-61.
• [11] Murillo-Arcila M. and A. Peris, Strong mixing measures for linear operators and frequent hypercyclicity, J. Math. Anal. Appl., 398 (2013), 462–465. [WoS]
• [12] Rudnicki R., Invariant measures for the flow of a first-order partial differential equation, Ergodic Theory Dynamical Systems, 8 (1985), 437–443.
• [13] Rudnicki R., Strong ergodic properties of a first-order partial differential equation, J. Math. Anal. Appl., 133 (1988), 14–26.
• [14] Rudnicki R., Chaos for some infinite-demensional dynamical systems, Math. Meth. Appl. Sci. 2004, 27,723-738.
• [15] Rudnicki R., Chaoticity of the blood cell production system, Chaos: An Interdisciplinary Journal of Nonlinear Science, 19 (2009), 043112, 1–6.
• [16] Rudnicki R., An ergodic theory approach to chaos, Discrete Contin. Dyn. Syst. A 35 (2015), 757–770.
• [17] Takeo F., Chaos and hypercyclicity for solution semigroups to some partial differential equations, Nonlinear Analysis 63, 2005, e1943 - e1953.
• [18] Takeo F., Chatoic or hypercyclic semigroups on a function space C0 .I;C/ or Lp .I;C/, SUT Journal of Mathmatics, Vol 41, No 1, 2005, 43-61.

Identyfikatory

DOI

10.1515/math-2015-0036